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Year 7

Divisibility tests for 2 and 3

I can identify and explain whether a number is or is not a multiple of a given integer.

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Year 7

Divisibility tests for 2 and 3

I can identify and explain whether a number is or is not a multiple of a given integer.

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Lesson details

Key learning points

  1. Any even number is a multiple of 2.
  2. For any multiple of 3 the sum of its digits is also a multiple of 3.

Keywords

  • Divisibility - Divisibility is a number’s ability to be exactly divided by another number, leaving no remainder.

Common misconception

Incorrectly summing the digits of an integer to identify a multiple of 3.

Use number bonds to sum large numbers of digits.


To help you plan your year 7 maths lesson on: Divisibility tests for 2 and 3, download all teaching resources for free and adapt to suit your pupils' needs...

When talking about multiples of 2, go around the class and challenge the students to give a multiple of 2 greater than the previous person. When doing the multiples of 3 students could come to the board and make a list of examples and non-examples.
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This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
What are the first five multiples of 11?
Correct answer: 11, 22, 33, 44, 55
1, 11
1, 2, 5.5, 11
22, 33, 44, 55, 66
Q2.
Match an example of a common multiple of the numbers given.
Correct Answer:Common multiple of 2 and 3,are multiples of 6
tick

are multiples of 6

Correct Answer:Common multiple of 2 and 5,are multiples of 10
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are multiples of 10

Correct Answer:Common multiple of 3 and 5,are multiples of 15
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are multiples of 15

Correct Answer:Common multiple of 7 and 11,are multiples of 77
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are multiples of 77

Q3.
Identify the common multiples of 2 and 7.
1, 2, 7
2, 4, 6, 7, 8, 10, 12, 14, ….
Correct answer: 14, 28, 42, 56, ….
There are no common multiples of 2 and 7
Q4.
Identify the common multiples of 3, 4, and 5
1, 2, 4, 5, 10
Correct answer: 60, 120, 180, ….
3, 4, 5, 6, 8, 10, ….
There are no common multiples of 3, 4 and 5
Q5.
A light flashes every 4 minutes. Another light flashes every 5 minutes. At 9 am, they flash at the same time. What time will they next flash together?
9:14 am
9:09 am
9:15 am
Correct answer: 9:20 am
Q6.
Starting with the largest, put these fractions in order of size. Use a common denominator to help you.
1 - $${5} \over {6}$$ 
2 - $${2} \over {3}$$ 
3 - $${1} \over {2}$$ 
4 - $${7} \over {15}$$ 
5 - $${1} \over {10}$$ 

Exit quiz

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6 Questions

Q1.
__________ is a number’s ability to be exactly divided by another number, leaving no remainder.
Squaring
Cubing
Correct answer: Divisibility
Multiplying
Q2.
Sofia says, "All multiples of 2 are even." Is Sofia's statement sometimes true, always true or never true?
Sometimes true
Correct answer: Always true
Never true
Q3.
Jun says, "All common multiples of 3 and 5 are even." Is Jun's statement sometimes true, always true or never true?
Correct answer: Sometimes true
Always true
Never true
Q4.
Match each description of a multiple with the correct divisibility test.
Correct Answer:For any multiple of 3:,the sum of the digits is a multiple of 3
tick

the sum of the digits is a multiple of 3

Correct Answer:For any multiple of 2:,the digit in the ones column is always a 0, 2, 4, 6 or 8
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the digit in the ones column is always a 0, 2, 4, 6 or 8

Correct Answer:For any multiple of 2 and 3:,the number is even and sum of the digits is a multiple of 3
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the number is even and sum of the digits is a multiple of 3

Q5.
All common multiples of 2 and 3 are:
multiples of 5
Correct answer: multiples of 6
multiples of 8
multiples of 10
Q6.
Match each number with the correct statement.
Correct Answer:377 037 ,is a multiple of 3
tick

is a multiple of 3

Correct Answer:372 950,is a multiple of 2
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is a multiple of 2

Correct Answer:48 959,is not a multiple of 2 or 3
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is not a multiple of 2 or 3